solve each proportion. if necessary, round to the nearest hundredth.\n10. \\( \\frac { 2 b + 14 } { 8 } =…

solve each proportion. if necessary, round to the nearest hundredth.\n10. \\( \\frac { 2 b + 14 } { 8 } = \\frac { 1 - 2 b } { 12 } \\)\n11. \\( \\frac { 2 z - 3 } { 3 } = \\frac { 3 z - 1 } { 6 } \\)\n12. \\( \\frac { 9 } { - t - 6 } = \\frac { 27 } { 2 t + 22 } \\)\n13. \\( \\frac { 6 } { 4 y + 1 } = \\frac { 9 } { 9 y - 6 } \\)

solve each proportion. if necessary, round to the nearest hundredth.\n10. \\( \\frac { 2 b + 14 } { 8 } = \\frac { 1 - 2 b } { 12 } \\)\n11. \\( \\frac { 2 z - 3 } { 3 } = \\frac { 3 z - 1 } { 6 } \\)\n12. \\( \\frac { 9 } { - t - 6 } = \\frac { 27 } { 2 t + 22 } \\)\n13. \\( \\frac { 6 } { 4 y + 1 } = \\frac { 9 } { 9 y - 6 } \\)

Answer

Explanation:

Step1: Cross - multiply

For the proportion (\frac{2b + 14}{8}=\frac{1-2b}{12}), cross - multiplying gives (12(2b + 14)=8(1 - 2b)). Using the distributive property (a(b + c)=ab+ac), we have (24b+168 = 8-16b).

Step2: Move variables to one side

Add (16b) to both sides: (24b + 16b+168=8-16b + 16b), which simplifies to (40b+168 = 8).

Step3: Move constants to the other side

Subtract (168) from both sides: (40b+168-168 = 8-168), so (40b=-160).

Step4: Solve for (b)

Divide both sides by (40): (b=\frac{-160}{40}=-4).

Answer:

(b = - 4)